the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}(2^5{:}s_{6})$ of $a(4)$ of index $63$‎.

the full automorphism group of $u_6(2)$ is a group of the form $u_6(2){:}s_3$. the group $u_6(2){:}s_3$ has a maximal subgroup $2^9{:}(l_3(4){:}s_3)$ of order 61931520. in the present paper, we determine the fischer-clifford matrices (which are not known yet) and hence compute the character table of the split extension $2^9{:}(l_3(4){:}s_3)$.

We define and study the ternary analogues of Clifford algebras. It is proved that the ternary Clifford algebra with N generators is isomorphic to the subalgebra of the elements of grade zero of the ternary Clifford algebra with N+1 generators. In the case N = 3 the ternary commutator of cubic matrices induced by the ternary commutator of the elements of grade zero is derived. We apply the terna...

A version of Henrici's classical perturbation theorem for eigenvalues of matrices is obtained for joint spectra of commuting tuples of matrices. The approach involves Clifford algebra techniques introduced by Mcintosh and Pryde.

‎the purpose of this paper is the determination of the inertia‎ ‎factors‎, ‎the computations of the fischer matrices and the ordinary‎ ‎character table of the split extension $overline{g}=‎ ‎3^{7}{:}sp(6,2)$ by means of clifford-fischer theory‎. ‎we firstly‎‎determine the conjugacy classes of $overline{g}$ using the coset‎ ‎analysis method‎. ‎the determination of the inertia factor groups of‎ ‎...

in this paper we first construct the non-split extension $overline{g}= 2^{6} {^{cdot}}sp(6,2)$ as a permutation group acting on 128 points. we then determine the conjugacy classes using the coset analysis technique, inertia factor groups and fischer matrices, which are required for the computations of the character table of $overline{g}$ by means of clifford-fischer theory. there are two inerti...

4 × 4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on any particular representation of the Dirac matrices (e.g. due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation ...

the subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called affine subgroups., the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}o^{-}_{6}(2...

We show that Clifford algebras are closely related to the study of isoclinic subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix problem. Isocliny angles are introduced to parametrize gamma matrices, i.e., matrix representations of the generators of finite-dimensional Clifford algebras C(m,n). Restricting the consideration to the Clifford algebra C(4, 0), this parametrizat...